Estimation of unconfined aquifer parameters by genetic algorithms

摘要

Unconfined aquifer parameters, viz. transmissivity, storage coefficient, specific yield and delay index from a pumping test are estimated using the genetic algorithm optimization (GA) technique. The parameter estimation problem is formulated as a least-squares optimization, in which the parameters are optimized by minimizing the deviations between the field-observed and the model-predicted time-drawdown data. Boulton's convolution integral for the determination of drawdown is coupled with the GA optimization technique. The bias induced by three different objective functions: (a) the sum of squares of absolute deviations between the observed and computed drawdown; (b) the sum of squares of normalized deviations with respect to the observed drawdown; and (c) the sum of squares of normalized deviations with respect to the computed drawdown, is statistically analysed. It is observed that, when the time-drawdown data contain no errors, the objective functions do not induce any bias in the parameter estimates and the true parameters are uniquely identified. However, in the presence of noise, these objective functions induce bias in the parameter estimates. For the case considered, defining the objective function as the sum of the squares of absolute deviations between the observed and simulated drawdowns resulted in the best possible estimates. A comparison of the GA technique with the curve-matching procedure and a conventional optimization technique, such as the sequential unconstrained minimization technique (SUMT), is made in estimating the aquifer parameters from a reported field pumping test in an unconfined aquifer. For the case considered, the GA technique performed better than the other two techniques in parameter estimation, with the sum-of-squares errors obtained from the GA about one fourth of those obtained by the curve matching procedure, and about half of those obtained by SUMT.